The Gorgias Problem: Why Seeming Is Cheaper Than Being
My main focus is still on the Gorgias Problem:
It takes less energy to make something seem than it does to make it really be.
With regards to information movement this becomes:
It take less energy to make a person convicted of a belief than it does to make them understand.
Gorgias Problem = Shallowness Discounting
This problem needs renaming as Lincoln Sayger and Defender have argued. For now, I’m thinking of naming it ‘Shallowness Discounting’ because shallowness is an apt metaphor for seeming, and discounting points to the fact that it costs less resources than depth. I’m not sure it’s the best name because shallowness implies a weakness, but one can have incredibly strong conviction without understanding. All suggestions welcome.
Richard Skemp on Shallowness Discounting in Math Education
In the context of education I’ve been reading “The Psychology of Learning Mathematics” by Richard Skemp. Good book, I’ll probably read some more of his work. You can get the gist of his direction by reading this great paper on mathematics. He makes a distinction between automatic vs mechanical skill. The idea is simple. At first, there is a big gap between someone who is trying to understand and gain conceptual knowledge and someone who is working on sheer symbolic manipulation. The conceptual learner is much slower, spending lots of time and energy to understand what is happening here. In contrast, the symbolic manipulator will quickly be able to solve problems that fit the structure taught; they are gaining a mechanical skill. But the conceptual learner, with practice, will gain such fluency that they will be able to do the skill automatically. The Shallowness Discounting at work in math education! But notice another mess, that for an unsuspecting observer, the automatic and mechanical mathematicians look identical. And even tests won’t catch who is doing which. It’s only when you raise the bar and ask a new type of problem that the difference surfaces. But just read his 8 page paper above and enjoy.
Vygotskyian Pseudo-Concepts—Good or Bad?
I’m also always circling back to Vygotsky’s concept of pseudo-concepts1 and how shallowness can serve the creation of depth. My hunch is that pseudo-concepts can be useful in discovering a concept, but that there is a difference between pseudo-concepts that are reality formed vs those that are symbolically formed. Two different kinds of pseudo-concepts, if you will. So as you are trying to figure out a concept and watching reality, you’re likely to conceive of pseudo-concepts on the way, and this is fine (what Vygotsky noted). For example, you might come to think that emotional resonance is the criteria for good decision making. And then later on, you’ll see that this concept is actually false, and that it’s only one factor to be weighed, but not the actual criteria for a good decision. But if you are building pseudo-concepts through symbolic manipulation, there’s some sort of block that makes your mistake not only misleadingly conducive, but also restraining for getting to the true (or better) concept. I get stuck here with some hunch that people who use symbolic manipulation end up distorting their operating system in a way that makes their contact with reality worse. Really not sure what to make of that.
Socrates, Egan and I
I am convinced that a method for educating past the Gorgias Problem is via Socratic Conversations, as pioneered by Socrates! And as a tool for teaching children by Michael Strong. I designed and taught a Socratic Parenting Course with Michael in the past, and I have been thinking about how to create a better and more user-friendly presentation of the craft. For that, I’m working with Alessandro Gelmi, and using Egan’s ideas to help map out what is going on here.
Metaphors for Knowledge
Lastly, (but actually quite frequently,) I’ve been thinking a lot about the nature of knowledge and how different metaphors capture different aspects. I’m currently enjoying this contrast
Seeing vs. Having
Being immersed in a knowledge field vs. containing a knowledge field
Standing in wonder/awe/horror vs. pride
Boundlessness of knowledge vs scarcity
I greatly encourage you to go out and see if you can apply these metaphors to yourself and your own stance towards knowledge.
Well, that’s most of it. Any feedback, encouragement, critique, or whatever welcome!
From Gemini: “Vygotsky's pseudoconcept is a transitional stage in concept formation where a child uses a word or sign with superficial similarities to an adult's true concept but lacks the underlying logical, abstract understanding; it's a functional, associative grouping (like a "complex") that bridges chaotic early thinking and genuine conceptual mastery, allowing social communication before full comprehension. These pseudoconcepts, built from shared signs and social interactions, are crucial steps toward forming abstract, scientific concepts, even if initially based on concrete associations (color, shape, etc.) rather than deep meaning.” It’s not exactly how I would frame it, but good enough.
If you'll indulge me to make some assertions that I can't fully justify in the moment - I think there is a common theme to our thinking, which I will call incremental satisficing in conceptual space.
Satisficing is traditionally thought of as creating good enough solutions to problems. The idea here is to apply it to the concepts we form during education. That is, maybe it's okay to give a person a concept that is "wrong" from a higher vantage point, but functional, because it can be considered just a step on the ladder to enlightenment.
My recent post on the Glitch Gremlin is an example of this. You might perhaps want to never need gremlins. Ideally, you want to simply know the optimal way to apply your capabilities to all problems, and assign the optimal amount of emotional regret to yourself and others when you make a mistake or suboptimal choice. That Ultimate Optimal solution might not involve gremlins, but the "good enough solution for now" might.
I also think the Ultimate Optimal solution might actually involve gremlins. I'm not totally discounting that possibility!
About time that I caught up on your posts a bit 💪 I'll probably have several comments. I'll fire them off as I think of them.
My first is on the Gorgias Problem. This problem is induced by incomplete specification + optimization. In other words, it is almost ALWAYS the case that when you specify an optimization problem incompletely, the best solution will NOT be exactly what you want.
This is a fundamental, universal problem that extends all the way to things like fitting lines to data by least squares. The "best" solution, in the sense of minimizing squared error, is almost never the true solution, because the unknown truth cannot be included as a constraint in the specification.
This is the wellspring of many strange phenomena. For example, it's long been known in machine learning research that it can be beneficial to stop early when optimizing the fit of a model to data, because fully optimizing the fit eventually sends you past (the closest approach to) what you wanted and into the regime where you're overfitting, making the solution worse while still improving the optimization criterion.